Word (.docx)
Acrobat (.pdf)
Examples
Tamika can read 500 words in 3 minutes. Her reading rate can be described as
which is equivalent to the unit rate of 
words per minute.
Clarifications
Clarification 1: Instruction includes using manipulatives, drawings, models and words and making connections between ratios, rates and unit rates.Clarification 2: Problems will not include conversions between customary and metric systems.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Rate
- Unit Rate
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In grade 5, students represented the division of two whole numbers as a fraction. In doing this, students started to work with a ratio relationship that relates parts to wholes. In grade 6, students extend this concept to include rates, which are ratios between quantities that are most often in different units. Students use ratio relationships to describe unit rates and percentage relationship and use the division of positive rational numbers to calculate unit rates from rates. In grade 7, students learn that a unit rate is the same as a constant of proportionality in a proportional relationship between two variables.- Instruction connects rate and unit rate to student understanding of equivalent fractions from elementary school in both numeric and picture or model forms. Students can use the models to represent the situations in different ways (MTR.5.1).
- Allow student flexibility in accepting both simplified and non-simplified responses for rates unless unit rate is the specified or expected form.
Common Misconceptions or Errors
- Students may incorrectly identify what is being compared or the order of quantities being compared by the rate.
- Students may have difficulty connecting a unit rate, which is represented by a single number, to a ratio or non-unit rate, which may be represented by two numbers.
Strategies to Support Tiered Instruction
- Instruction includes the use of manipulatives and models to represent the provided rates and then to use multiplicative reasoning to determine the rate of one unit. Manipulatives and models include snap cubes, marbles, bar models, number lines or rate tables to help visually represent the relationship.
- Instruction includes the use of manipulatives to allow for students to explore the meaning of a unit rate. The teacher should provide two different counters to represent a rate equivalent to a whole number unit rate and then co-model the division of the counters into equal groups to determine how many counters of one color are needed to represent a single counter of the other color.
- For example: At the grocery store, you paid $9.00 for 3 pounds of apples. What is the unit price paid per pound of apples?
- For example: At the grocery store, you paid $9.00 for 3 pounds of apples. What is the unit price paid per pound of apples?
Instructional Tasks
Instructional Task 1 (MTR.6.1, MTR.7.1)In buying ground beef for hamburgers, there are several packages from which to choose as shown in the table below.
- Part A. Predict how much it would cost for a pound of beef. Explain why your prediction is reasonable.
- Part B. What is the unit cost of the ground beef? Does the unit cost differ by the package size at this store?
Instructional Task 2 (MTR.4.1)
The Jones family is planning on expanding their garden so that they can plant more vegetables. The ratio of the area of the old garden to the area of the new garden is 4¼:8 ¾. Convert this ratio to a unit rate and explain what it means in this context.
Instructional Task 3 (MTR.2.1, MTR.4.1, MTR.5.1)
- Part A. In your group, use the chart below to determine the rate and unit rate in miles per minute.
- Part B. Which form would be most efficient for this context? Why?
Instructional Items
Instructional Item 1At the grocery store, you paid $9.87 for 3.3 pounds of apples. What is the unit price paid per pound of apples?
Instructional Item 2
Brenda wants to buy one of the three cereals listed below. Determine which box is the best buy. Show and explain how you determined this.
- 16 ounces of Frosted Flurries for $3.50
- 12.4 ounces of Chocolate O’s for $2.42
- 11.5 ounces of Cinnamon Grahams for $2.35
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Expert
Perspectives Video: Professional/Enthusiasts
Perspectives Video: Teaching Idea
Problem-Solving Tasks
Tutorials
STEM Lessons - Model Eliciting Activity
This MEA requires students to formulate a comparison-based solution to a problem involving choosing the BEST daycare based upon safety, playground equipment, meals, teacher to student ratio, cost, holiday availability and toilet training availability. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client. Students will receive practice on calculating a discount, finding the sum of the discounts, working with ratios and ranking day cares based on the data given.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
In this MEA, students will apply the concepts of heat transfer, especially convection. Students will analyze factors such as temperature that affect the behavior of fluids as they form convection currents.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
Students are presented with the task of evaluating several types of fabric based on each of its characteristics. They need to analyze their current uniform needs and decide by choosing which type of fabric will best fit their uniform needs. Then they have to write a report explaining the procedure they used to analyze their choices, reasoning for their ranking and make the requested recommendations.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
This Model Eliciting Activity (MEA) is written at a 6th grade level.
This MEA asks the students to decide on a lawn mower that will provide the Happy Lawns: Lawn Care Service with the best value for their money. Students are asked to rank order the lawn mowers in term of gas tank capacity, customer rating, speed, amount of time the mower takes to cut an acre of grass, shipping, and cost of the lawn mower. Students must provide a "Best Value" lawn mower to the company owner and explain how they arrived at their solution.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
Students are asked to evaluate and test several rocket fin designs to determine the most effective design. After launch, the students are asked to test an additional design and also design their own rocket fin. Additionally, students will record and graph their results.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
In this Model Eliciting Activity, MEA, the students will rank the local produce markets by using qualitative and quantitative data. The students will have to calculate unit rates of produce prices and then compare and order them.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will choose the best location for a family relocating and will find the monthly costs per month to make the best decision.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
In this MEA students will use problem-solving strategies to determine which car to recommend to Americans living in India.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
This activity engages the students into time scheduling, budgeting, and decision making to maximize time efficiency.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx.
MFAS Formative Assessments
Students write and explain the meaning of a ratio and corresponding unit rate in the context of a word problem.
Students are asked to compute and interpret unit rates in two different ways from values that include fractions and mixed numbers.
Students are asked to explain the meaning of given rates and identify any that are unit rates.
Students are asked to convert a ratio of mixed numbers to a unit rate and explain its contextual meaning.
Students are given verbal descriptions of rates and asked to write them as unit rates.
Original Student Tutorials Mathematics - Grades 6-8
Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial.
Student Resources
Original Student Tutorial
Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial.
Type: Original Student Tutorial
Perspectives Video: Professional/Enthusiast
<p>An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings.</p>
Type: Perspectives Video: Professional/Enthusiast
Problem-Solving Tasks
The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?
Type: Problem-Solving Task
Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context.
Type: Problem-Solving Task
Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time.
Type: Problem-Solving Task
Tutorials
This video demonstrates finding a unit rate from a rate containing fractions.
Type: Tutorial
Watch as we solve a rate problem finding speed in meters per second using distance (in meters) and time (in seconds).
Type: Tutorial
This video demonstrates solving a unit price problem using equivalent ratios.
Type: Tutorial
In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.
Type: Tutorial
Parent Resources
Perspectives Video: Professional/Enthusiast
<p>An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings.</p>
Type: Perspectives Video: Professional/Enthusiast
Problem-Solving Tasks
The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?
Type: Problem-Solving Task
Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context.
Type: Problem-Solving Task
Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time.
Type: Problem-Solving Task
